Minimum value in each row of an implicitly-defined totally monotone matrix (Minimum value in each row of an implicitly-defined totally monotone matrix)
Revision as of 11:21, 15 February 2023 by Admin (talk | contribs) (Created page with "{{DISPLAYTITLE:Minimum value in each row of an implicitly-defined totally monotone matrix (Minimum value in each row of an implicitly-defined totally monotone matrix)}} == Description == Given a totally monotone matrix $A$ whose entries $A(i, j)$ are implicitly defined by some function $f(i, j)$ (assume $f$ takes constant time to evaluate for all relevant $(i, j)$), determine the minimum value in each row. == Parameters == <pre>n, m: dimensions of matrix; assume m...")
Description
Given a totally monotone matrix $A$ whose entries $A(i, j)$ are implicitly defined by some function $f(i, j)$ (assume $f$ takes constant time to evaluate for all relevant $(i, j)$), determine the minimum value in each row.
Parameters
n, m: dimensions of matrix; assume m≥n possibly uses a function f to define entries; assume evaluation of f takes time O(1)
Table of Algorithms
| Name | Year | Time | Space | Approximation Factor | Model | Reference |
|---|---|---|---|---|---|---|
| Naive algorithm | 1940 | $O(nm)$ | $O({1})$ auxiliary | Exact | Deterministic | |
| SMAWK algorithm | 1987 | $O(n({1}+log(n/m)$)) | $O(n)$ auxiliary? | Exact | Deterministic | Time |
| Divide and Conquer | 1987 | $O(m*log(n)$) | $O(log(n)$) auxiliary? | Exact | Deterministic | Time |
Time Complexity graph
Space Complexity graph
Pareto Decades graph
